The term radio propagation channel is commonly used in literature to characterize the complete radio transmission system from the transmitter to the receiver. Some relevant factors influencing the radio channel are the effects of (multipath) propagation, the antenna arrays and the rest of the radio equipment.
A MIMO radio channel can be compactly expressed using the notion of channel matrix:y=Hx+n   (1)where y is the received signal, x is the transmitted signal, H is the channel matrix and n is Gaussian noise. The interference caused by other users in the same frequency band is often included in the noise. The channel matrix describes the amplitude and phase change over the whole propagation channel between a pair of transmitter and receiver antennas (antenna arrays made of antenna elements). Each element of the matrix comprises the superposition of individual propagation paths, and the effects of corresponding antenna elements and other radio equipment.
In real-world situations, the channel matrix also includes, for example, the coupling between antenna elements. However, without further a priori information it does not allow separation of different aspects of the propagation.
In modern digital radio communications, the protocols often require knowledge about the channel matrix, or some parameters of it, and therefore it is usually measured. The measurement of the channel matrix is called channel estimation. Typically, and especially in mobile networks, channel estimation is based on reference symbols. Reference symbols are data symbols whose values, transmit times and frequencies are known in advance by the receiver. The simplest method for channel estimation is then to construct a least squares problem out of these symbols. The channel estimate is usually called Channel State Information (CSI).